Sintered polycrystalline terbium aluminum garnet and use thereof in magneto-optical devices

ABSTRACT

A composition is provided that includes a plurality of calcined particles of terbium aluminum oxide having a mean particle domain size of between 30 and 600 nanometers. A translucent article having a surface includes polycrystalline terbium aluminum garnet having a mean grain size from 1 to 10 microns and light scattering inclusions of aluminum-rich oxide and/or terbium-rich oxide that are present at less than 2 surface area percent of the surface. A process for forming such an article involves sintering the above provided composition at a temperature between 1500° C. and 1700° C. to yield a sintered article. The article has improved translucency and even transparency as sintering is performed under vacuum at a temperature between 1610° C. and 1680° C. Hot isostatic pressing alone or in combination with article polishing also improves article translucency.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application is a divisional of U.S. patent application Ser. No.11/399,198 filed Apr. 6, 2006, now U.S. Pat. No. 7,427,577.

FIELD OF THE INVENTION

The present invention relates to polycrystalline terbium aluminum garnet(“TAG”) manufactured by sintering of nanoparticles of terbium aluminumoxide of defined composition, and to magneto-optical devices employingthe polycrystalline TAG.

BACKGROUND OF THE INVENTION

Materials having magneto-optical properties are well known. Simpleglasses such as borosilicate crown glass, for example, are known torotate the plane of polarized light when placed in a magnetic field. Therotation achieved (θ) is proportional to the length of the light path,l, the strength of the magnetic field B, and a magneto-optical materialdependent parameter known as the Verdet constant K:θ=BKl.The Verdet K constant may have dimensions of min·Oe⁻¹·cm⁻¹, forinstance. The rotation of light is called the Faraday effect.

Borosilicate glass has a rather low Verdet constant, and thusmanufacture of devices such as Faraday rotators, isolators, modulators,etc., would require either or both of a very long path length and a verystrong magnetic field. High density lead-containing glasses such as theheavy flints have a Verdet constant some four times larger thanborosilicate glass, but still too low for practical magneto-opticaldevices. Doping such glasses with elements with high magnetic momentssuch as terbium increases the Verdet constant, but the value is stilllower than desired, and large aperture devices are especiallyimpractical, due to the difficulty of establishing the necessary verystrong magnetic field across the device. Thus, it would be mostdesirable to provide materials which are translucent and which have ahigh Verdet constant.

F. J. Sansalone, “Compact Optical Isolator,” Applied Optics, 10, No. 10pp. 2329-2331 (October 1971) describes the use of crystalline TAG toproduce a compact optical isolator. The magnetic field necessary forthis small aperture device was able to be produced by rare earth buttonmagnets. According to Sansalone, TAG has a Verdet constant which is anorder of magnitude higher than lead glass. C. B. Rubenstein, et al.,“Magneto-Optical Properties of Rare Earth (III) Aluminum Garnets,” J.App. Phys., 35 p. 3069-70 (1964), measured the Verdet constants ofseveral rare earth aluminum garnets, and found TAG to have the highestVerdet constant of those tested. Thus it appears that TAG would be thematerial of choice for magneto-optical devices, and yet only small andsometimes thin film devices have been constructed.

In U.S. Pat. No. 5,245,689, TAG has been proposed as one of twoepitaxially deposited garnet layers in a magneto-optical waveguide,although no devices employing TAG seem to have been created. U.S. Pat.No. 6,580,546 describes that Faraday rotators are activated by anelectromagnet; the device also containing semi-hard magnetic materialsto enhance latching and to decrease the drive current necessary to causeswitching. While TAG is again mentioned, no device employing TAG appearsto have been constructed. The same applies to U.S. Pat. No. 6,493,139,which discloses TAG as useful for optical switches.

The reason that TAG has not been used in practical magneto-opticaldevices of any size is the difficulty of providing single crystalmaterials. As indicated by Oliver et al. U.S. Pat. No. 6,144,188,polycrystalline garnet films may be prepared by chemical vapordeposition followed by annealing. However, these polycrystalline filmsdo not share the optical transmission characteristics of single crystalmaterial, and are thus useful only in certain applications. Rubenstein,in 1964, grew TAG crystals measuring 3 millimeters on a side bycrystallization from lead oxyfluoride flux in platinum crucibles. Theflux was removed from the solidified mass using nitric acid. Theprocedure uses toxic ingredients and has not been amenable tocommercialization. Despite the fact that Rubenstein states that crystalsmeasuring several centimeters on a side are grown by this technique,Sansalone, seven years later, described a Faraday rotator of TAG singlecrystal provided by Rubenstein, and bemoaned the fact that the longestcrystalline rod was only 1 centimeter long. With this 1 centimeter TAGrod, and rare earth magnets, a rotation of about 31° was obtained at6328 Å, and a full 45° rotation could be achieved at wavelengths shorterthan about 5000 Å. Longer crystals could have achieved 45° rotation atlonger wavelengths, but were apparently unavailable.

M. Geho et al., “Growth of terbium aluminum garnet (Tb₃Al₅O₁₂; TAG)single crystals by the hybrid laser floating zone machine,” Journal ofCrystal Growth 267, p. 188-193 (2004) discloses that TAG showsincongruent melting behavior, which prevent large size crystal growth.Instead of growing single crystals by conventional techniques, Geho useda special floating zone (“FZ”) method of crystal growth, by stackingalternating sheets of aluminum oxide and terbium oxide followed bysintering to produce a porous stack. This stack was then heated in afloating zone furnace having four CO₂ lasers arranged radially aroundthe rod shaped green body, and assisted by four quartz halogen lampssimilarly arranged. However, while the length of the crystal does notappear to be limited in such a method, the crystal diameter is only 3millimeters.

Thus, there exists a need for TAG magneto-optical devices in largeaperture sizes, and with full rotation at all relevant wavelengths.There also exists a need for TAG precursors to form translucent ortransparent TAG devices.

SUMMARY OF THE INVENTION

A composition is provided that includes a plurality of calcinedparticles of terbium aluminum oxide having a mean particle domain sizeof between 30 and 600 nanometers.

A translucent article includes polycrystalline terbium aluminum garnethaving a mean grain size from 1 to 10 microns and light scatteringinclusions of aluminum-rich oxide and terbium-rich oxide that arepresent at less than 2 surface area percent of the surface. A processfor forming such an article involves sintering the above providedcomposition at a temperature between 1500° C. and 1700° C. to yield asintered article. The article has improved translucency and eventransparency as sintering is performed under vacuum at a temperaturebetween 1610° C. and 1680° C. Hot isostatic pressing alone or incombination with article polishing also improves article translucency totransparency.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a photograph of terbium aluminum oxide formed according to theprocedure of Example 1 overlying graphical text “TAG” to illustratetranslucency;

FIG. 2 is a photograph of terbium aluminum oxide formed according to theprocedure of Example 2 overlying graphical text “TAG” to illustratetranslucency;

FIG. 3 is a photograph of terbium aluminum oxide formed according to theprocedure of Example 3 overlying graphical text “TAG” to illustratetranslucency;

FIG. 4 is a photograph of terbium aluminum oxide formed according to theprocedure of Example 4 overlying graphical text “TAG” to illustratetranslucency;

FIG. 5( a) is a photograph of terbium aluminum oxide formed according tothe procedure of Example 5 overlying graphical text “TAG” to illustratetranslucency prior to hot isotactic pressing;

FIG. 5( b) is a photograph of terbium aluminum oxide formed according tothe procedure of Example 5 overlying graphical text “TAG” to illustratetranslucency after hot isotactic pressing; and

FIG. 6 is a photograph of terbium aluminum oxide formed according to theprocedure of Example 6 overlying graphical text “TAG” to illustrate.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

The present invention has utility as a precursor composition for atranslucent terbium aluminum garnet (TAG) article. Through theproduction of a polycrystalline TAG article with magneto-opticalproperties suitable for device formation, difficulties associated withgrowing a TAG single crystal with preselected dimensions greater than 3millimeters is overcome. An inventive precursor composition issynthesized and processed so as to inhibit formation of optically lightscattering inclusions. Through control of sintering conditions andsubsequent processes to densify and polish an article, apolycrystalline, transparent TAG article is formed that is particularlywell suited for use as a magneto-optical element such as a Faradayrotator, optical isolator, or magneto-optical waveguide.

A precursor composition for a polycrystalline TAG article includescalcined terbium aluminum oxide particles that have a mean particledomain size of between 30 and 600 nanometers. The precursor particles ifcalcined at a comparatively low temperature of 700 to 800° C. for aduration of a few hours retains a crystal structure in the particlescomparable to YAlO₃ (powder diffraction pattern 74-1334) and withoutintending to be bound by a particular theory is believed to be ahexagonal phase. Preferably, the mean hexagonal structure terbiumaluminum oxide has a mean particle domain size of between 30 and 200nanometers. It is appreciated that the hexagonal phase terbium aluminumoxide may well include secondary amorphous phases or secondary crystalstructure forms illustratively including (A_(3/4)B_(1/4))BO₃.Additionally, it is appreciated that the terbium:aluminum stoichiometricatomic ratio is maintained at 3±0.01:5±0.01 in order to achievestoichiometric TAG having a formula Tb₃Al₅O₁₂. It is appreciated thatstoichiometric deviations in the terbium:aluminum atomic ratio away fromthat of TAG results in the formation of aluminum-rich oxide orterbium-rich oxide inclusions, depending on the excess metal.Aluminum-rich oxide and terbium-rich oxide are both light scatteringmaterials and enhance the opacity of the resulting TAG article.

Optionally, a precursor composition is formulated with a fraction of theterbium atoms replaced with a metal M¹ where M¹ is Y, La, Gd, Lu orother rare earth element. Similarly, a fraction of the aluminum atoms ofTAG are substituted with a metal M² where M is Sc, Ga, In or trivalenttransition metal Additionally, it is appreciated that a portion ofterbium atoms is replaced with M¹ while simultaneously a portion ofaluminum atoms are replaced with metal M² to yield a substituted TAGcomposition having the formulation:(Tb_(3-x)M_(x) ¹)_(α)(Al_(5-y)M_(y) ²)_(β)O₁₂where x and y each independently range from 0 to 0.1, 3α is 3±0.01 and5β is 5±0.01. More preferably, x and y each independently range in valuefrom 0 to 0.05, and most preferably range from 0 to 0.01. Suchsubstituent metals are added to modify the magnetic and/or opticalproperties of the resulting TAG article or provided to suppressformation of aluminum-rich oxide or terbium-rich oxide inclusion bodies.

A precursor composition is formed by calcining terbium aluminum oxideparticles with a preselected terbium:aluminum stoichiometric atomicratio at a temperature between 700° C. and 1300° C. The terbium aluminumoxide (TAO) particles as synthesized are noted to by X-ray powderdiffraction to have a partially amorphous structure with lesser quantityhexagonal crystal structure material. With calcinations in the range of500° C. to 700° C., the TAO exhibits predominantly a hexagonal crystalstructure that converts to a garnet crystal structure with highertemperature range calcination. A transitory orthorhombic crystalstructure phase is noted therebetween for some TAO powders duringcalcinations as shown in Table 1. The calcinations temperature and timeneeded for phase converting depend on the method of making originalparticles, such as precursors and reactor conditions.

TABLE 1 Calcination for TAG powder Phase Calcined TAG PrecursorComposition Percentage AP 800° C. 1000° C. 1100° C. 1100° C. 1100° C.1200° C. (%) Powder 2 hours 1 hour 1 hour 2 hours 3 hours 1 hour TAO-100 100 93 0 0 0 0 hexagonal TAO- 0 0 7 48.6 35 25 0 orthorhombic TAG 00 0 51.4 65 75 100 Mean 73 56 65 87 88 109 171 particle size (nm)

The increase in the mean particle domain size observed in calcinationfor 3 hours at 1100° C. and 1 hour at 1200° C. in Table 1 has associatedtherewith a necking phenomenon indicative of material flow betweencontiguous particles. The extent of this phenomenon can vary with theinitial crystallinity and surface chemistry of starting particles.

A terbium aluminum oxide (TAO) particulate having an amorphous orhexagonal crystal structure and a preselected terbium:aluminum atomicratio prior to calcination is produced by a variety of conventionaltechniques. These techniques illustratively include flame pyrolysis,solution precipitation, and combination. Liquid phase flame spraypyrolysis represents a preferred method of terbium aluminum oxideparticulate synthesis. Liquid feed flame spray pyrolysis requiresterbium and aluminum precursors to be present in the form of a solutionor suspension. Suitable terbium aluminum oxide liquid feed flame spraypyrolysis precursors are solutions or suspensions of terbium- oraluminum-containing compounds illustratively including complexes ofcarboxylates such as acetates, propionates, alkyl(hexanoates); andalkoxides. Still further precursors and the formation thereof aredisclosed in U.S. Pat. No. 5,614,596 and PCT Publication WO 00/38282.Feeding such a precursor solution or suspension into a flame affordshighly uniform particulates of controlled size and composition. TypicalTAO particulate mean particle domain sizes range from 10 to 400nanometers with the particulates having a generally spherical shape.Larger particles often exhibit faceting and preferential surface growthalong low energy planes. Control of particulate domain size is exercisedthrough parameters such as precursor solution or suspension feed rate,liquid atomization droplet size, flame dwell time, and flametemperature.

Regardless of the synthesis method of terbium aluminum oxideparticulate, it is appreciated that stoichiometry adjustments can bemade between terbium-M¹-aluminum-M² through the addition of additionalparticulate rich in the underrepresented metal atom. As translucency andtransparency are dependent on limiting incorporation of light scatteringvoids and inclusions, preferably stoichiometry corrective addition tothe particulate also includes a homogeneous mixture of the various metalatoms produced as detailed above, as opposed to a pure aluminum oxide,or terbium oxide, M¹-oxide or M²-oxide. The resulting stoichiometricallymodified terbium aluminum oxide is then calcined in air at a temperaturebetween 700° C. and 1200° C. for a time duration ranging from 30 minutesto several hours to provide a more uniform oxygenation and atomic levelhomogeneity. In the course of calcination, an increase in particledomain size occurs with increased temperature and duration ofcalcination. The resulting calcined mass of agglomerated material isformed into an inventive precursor composition through conventionaltechniques such as sonication, ball milling, grinding, and combinationsthereof to form calcined particles of terbium aluminum oxide having amean particle domain size of between 30 and 600 nanometers. Preferably,the calcined particles have a mean particle domain size of between 40and 150 nanometers. More preferably, a collection of unimodal calcinedparticles, regardless of mean particle domain size, have sizedistribution such that less than 5 number percent of the particles liebeyond 2 sigma in the statistical distribution of particle size.

It is appreciated that conventional ceramic densification techniques areoperative herein to maximize green density of an article formed from theinventive precursor composition. These techniques include the use of aprecursor composition particle size distribution theoreticallyapproaching monodisperse, the use of bimodal distributions with modes ofsufficiently different sizes such that smaller particles are able tofill interstices between the larger mode particles, and multimodaldistributions.

A green body article is formed from a slurry in water or organic solventof calcined TAO particles. Organic solvents operative hereinillustratively include alkyl and aryl, where aryl solvents contain atleast carbon atoms: C₁-C₈ alcohols, C₂-C₈ ethers, C₂-C₁₂ ketones oraldehydes, C₃-C₂₀ esters; heterocyclic solvents such as tetrahydrofuranand pyridine. The TAO content of the slurry is typically from 20 to 80total slurry weight percent and preferably from 30 to 60 total slurryweight percent. Typically, the particles have a positive zeta potentialupon dispersion in water as a slurry.

Optionally, suitable fugitive binder is added to the slurry. A fugitivebinder is defined as a binder or the decomposition products thereof thatis removed during sintering to greater than 99 weight percent of thebinder present. Fugitive binders illustratively includepolyvinylpyrrolidones, polyvinyl alcohol, polyacrylates, latexes, andmineral oil. A preferred binder is polyvinyl alcohol. Binders aretypically present from 0 to 5 total slurry weight percent for pressmolding or slip casting, while tape casting binders are typicallypresent from 5 to 40 total slurry weight percent. It is appreciated thatslurry formation is promoted by sonication, especially in instanceswhere optional additives are provided.

Optionally, a dispersant is also added to the slurry. Dispersantsoperative herein illustratively include surfactants, with the nature ofthe surfactant as to nonionic, cationic, or anionic and thehydrophilic-lipophilic balance (HLB) thereof being dictated by factorsincluding the zeta potential of the precursor composition particles, andthe nature of the slurry solvent. Water represents a preferred slurrysolvent. Ammonium polymethacrylate, fructose, and polyoxyethylene glycolare representative specific dispersants. A dispersant is typicallypresent from 0 to 4 total slurry weight percent. Preferably, adispersant is selected to improve solid loading for dispersed precursorcomposition particles. Other conventional additives to a slurry includea thixotrope.

The slurry of calcined terbium aluminum oxide precursor compositionparticles are preferably filtered through a sieve or other filter mediaprior to formation of a green body to remove spurious contaminants andexcessively large agglomerates of terbium aluminum oxide that mightoperate to lessen purity and/or grain density of a resulting article.

An inventive article is formed from a slurry by conventional techniquesillustratively including dry pressing, slip casting, and tape casting.For dry pressing, it is appreciated that slurries are preferablysubjected to granulation to form a pre-consolidated powder. It isappreciated that in instances where an article is tape cast, that anextrudable tape casting binder is present in a quantity sufficient toallow convenient tape formation. Slip casting and tape casting areappreciated to be article formation techniques well suited for thecreation of complex forms and shapes that are especially difficult toform from conventional single crystal TAG. Optionally, cold isostaticpressing is employed to facilitate dimensionally uniform grain bodydensification. Typical cold isostatic pressing conditions includeexertion of 300 megapascals for 20 minutes.

Sintering of calcined terbium aluminum oxide particle precursorcomposition yields an inventive TAG article. Sintering accomplishes thepurpose of binder and other additive burnout, typically at temperaturesup to about 700° C., followed by elevated temperature sintering. Anexemplary temperature ramp for burnout is 1° C./min to 180° C., hold 5hours, then 0.5° C./min to 250° C., hold 1 hour, then 0.5° C. to 400° C.followed by 1° C./min to 500° C. Sintering temperatures range between1500° C. and 1700° C. with the atmosphere and duration of sinteringaffecting the sintering temperature. Sintering occurs under vacuum,inert atmosphere, in air, and in a reducing atmosphere. Optionally, hotisostatic pressing to facilitate densification is performed during, orsubsequent to sintering. Preferably, sintering occurs under vacuum.Owing to the tendency of TAG to disproportionate into aluminum-richoxide domains and terbium-rich oxide domains upon cooling from a melt,sintering at temperatures approaching the TAG melting temperature isdone with care.

Typical pressures for vacuum sintering are below 1 torr. Preferably,vacuum sintering pressures are below 10⁻³ torr with pressures of between10⁻⁵ and 10⁻⁶ torr being more preferable. Preferably, vacuum sinteringoccurs at more than 1600° C. for a duration of 1 to 6 hours. Morepreferably, vacuum sintering occurs for this time duration between 1610°C. and 1680° C. in order to lessen the inclusions. The area percentageof an inclusion is determined by measuring the two-dimensional areaassociated with an inclusion on a given plane of an inventive article.Typically, the plane used for a determination of inclusion areapercentage is the flat face of an 8 millimeter diameter pellet formedfrom an inventive precursor composition. Under these sinteringconditions, the mean grain size of TAG domains in a given plane is from1 to 10 microns and preferably between 1 and 5 microns. More preferably,the grain size is between 1 and 3 microns. It is noted that the grainsize of the sintered article tends to increase as the precursorscomposition calcinations temperature increase. These results aresummarized in Table 2.

Aluminum-rich oxide and/or terbium-rich oxide inclusions are present atless than 2 surface area percent of a given surface in order to afford atranslucent inventive article. Preferably, the inclusions are present atless than 0.5 surface area percent. Most preferably, the inclusions arepresent at less than 0.1 surface area percent.

TABLE 2 Microstructure of sintered TAG articles 1650° C.-3 hour vacuum1650° C.-3 hour vacuum sinter hexagonal structure sinter garnetstructure Property (TAO) precursor (TAG) precursor Grain size 1.78 4.25(microns) Grain feature Flat Flat Grain boundary Curved Curved Inclusionsize, 0.2-0.5 microns 0.3-0.5 microns area percentage 0.064% 0.07%Intergrain pores No No Article color Pale yellow Pale yellowTranslucency Yes Yes

The present invention is further detailed with reference to thefollowing non-limiting examples. In each instance terbium aluminum oxideparticles are synthesized by liquid feed flame spray pyrolysis andcharacterized by a predominant amorphous, hexagonal, or mixture thereofas crystallographic phase. The powder is dry sieved to exclude coarseagglomerates and impurities having a size of greater than 150 micron.The dry sieve powder is then calcined and formed as a slurry. The slurryis subjected to ball milling and/or ultrasonic agitation and then wetsieved. The dispersion of calcined precursor particles is then dried,dry sieved and formed into a pellet. The pellet is cold isostaticallypressed with 300 megapascals of force prior to being subjected to abinder burnout heating phase. After burnout of the binder and anydispersants that have been added, the resulting pellet is sintered andhot isostatically pressed. The results for Examples 1-6 are summarizedin Table 3 and corresponding images of FIGS. 1-6 showing a 1 centimeterdiameter pellet overlying the letter “A”.

TABLE 3 Process to Form Translucent TAG Calcinings Sintering HotIsostatic Precursor T(° C.)-t(h) Slurry atmosphere Press (HIP) ExamplePowder phase Composition Drying T(° C.)-t(h) T(° C.)-t(h) FIG. 1 TAOhexagonal phase 1100-1 40 g powder oven H₂/He 1670-4 1 orthorhombic- 60g DI H₂O 1650-6 garnet 0.4 g PVA 0.6 g PEG 2 TAO hexagonal phase 1100-140 g powder oven vacuum 1650-6 1670-4 2 orthorhombic- 60 g DI H₂O garnet0.4 g PVA 0.6 g PEG 3 TAO hexagonal phase 1100-1 40 g powder freezevacuum 1650-6 1670-4 3 orthorhombic- 60 g DI H₂O granulated garnet 0.4 gPVA freeze dried 0.6 g PEG 4 0.005% Ce doped TAO 800-2 hexagonal- 20 gpowder oven vacuum 1650-6 1670-4 4 hexagonal phase orthorhombic 45 g DIH₂O 0.4 g PVA 0.15 Darvan 5 TAO hexagonal phase 800-2 hexagonal- 40 gpowder milling 24 h, Pre-fire 1680-4 5a pre-HIP orthorhombic 60 g DI H₂Othen oven 1200-2 (air), 5b post-HIP 0.4 g PVA 1650-4 (vacuum) 0.4 g PEG0.4 g Darvan 6 TAO hexagonal phase 1000-3 hexagonal 40 g powder ovenvacuum 1650-6 1680-4 6 orthorhombic- 60 g DI H₂O garnet

Patent documents and publications mentioned in the specification areindicative of the levels of those skilled in the art to which theinvention pertains. These documents and publications are incorporatedherein by reference to the same extent as if each individual document orpublication was specifically and individually incorporated herein byreference.

The foregoing description is illustrative of particular embodiments ofthe invention, but is not meant to be a limitation upon the practicethereof. The following claims, including all equivalents thereof areintended to define the scope of the invention.

1. A composition comprising: a plurality of calcined particles ofterbium aluminum oxide having a mean particle domain size of between 30and 600 nanometers.
 2. The composition of claim 1 wherein said pluralityof particles have a hexagonal crystal structure.
 3. The composition ofclaim 1 wherein said plurality of particles have a terbium aluminumgarnet crystal structure.
 4. The composition of claim 1 wherein saidplurality of particles have a mixed crystal structure of orthorhombicand at least one crystal structure selected from the group consistingof: hexagonal and garnet.
 5. The composition of claim 1 wherein the meanparticle domain size is between 40 and 150 nanometers.
 6. Thecomposition of claim 5 wherein less than 5% of said plurality ofparticles is beyond two sigma for a statistical distribution for saidplurality of particles.
 7. The composition of claim 1 wherein saidplurality of particles has a net positive zeta potential upon dispersionin water.
 8. The composition of claim 1 further comprising a solvent inwhich said plurality of particles are slurried.
 9. The composition ofclaim 8 further comprising a dispersant.
 10. The composition of claim 8further comprising a fugitive binder.
 11. The composition of claim 8wherein said solvent is water.
 12. The composition of claim 1 whereinsaid plurality of particles are aggregated into multiple particleaggregates.
 13. The composition of claim 1 wherein said plurality ofparticles further comprise a metal ion substitute in the terbiumaluminum oxide represented by the formula(Tb_(3-x)M_(x) ¹)_(α)(Al_(5-y)M_(y) ²)_(β)O₁₂ where x and y eachindependently range from 0 to 0.1, 3α is 3±0.01 and 5β is 5±0.01, M¹ isa rare earth element and M² is scandium, gallium, indium or othertrivalent transition metal.